phy lab 1

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Physicist Peter's Custom Equation

Equation Family: Miscellaneous

y = A + B*(X-C) + 0.5*G*(X-C)**2

Wed Feb 5 17:00:58 2014 local server time

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Mark 6:53-56

And when they had passed over, they came into the land of Gennesaret, and drew to the shore. Andwhen they were come out of the ship, straightway they knew him, And ran through that whole regionround about, and began to carry about in beds those that were sick, where they heard he was. And

whithersoever he entered, into villages, or cities, or country, they laid the sick in the streets, andbesought him that they might touch if it were but the border of his garment: and as many as touched

him were made whole.

Read or search the King James Bible online athttp://quod.lib.umich.edu/k/kjv/


Coefficients

y = A + B*(X-C) + 0.5*G*(X-C)**2

Fitting target of lowest sum of squared absolute error = 3.5375377442728176E-06

A = 4.4802945381686374E-02

B = 9.1759653506420780E-01

C = 0.0000000000000000E+00

G = 9.6094939267681241E+00


Coefficient and Fit Statistics

Most statstics from scipy.odr.odrpack and http://www.scipy.org/Cookbook/OLS

LL, AIC and BIC from http://stackoverflow.com/questions/7458391/python-multiple-linear-regression-us

ing-ols-code-with-specific-data

Degrees of freedom (error): 10

Degrees of freedom (regression): 3

Chi-squared: 3.53753774427e-06

R-squared: 0.99995721381

R-squared adjusted: 0.999944377953

Model F-statistic: 77903.4248532

Model F-statistic p-value: 1.11022302463e-16

Model log-likelihood: 86.4728192195

AIC: -11.7818313171

BIC: -11.5992435086

Root Mean Squared Error (RMSE): 0.000502674116549

A = 4.4802945381686374E-02

std err squared: 1.97121E-07

t-stat: 1.00911E+02

p-stat: 2.22045E-16

95% confidence intervals: [4.38137E-02, 4.57922E-02]

B = 9.1759653506420780E-01


t-stat: 7.24855E+01

p-stat: 6.21725E-15

95% confidence intervals: [8.89390E-01, 9.45803E-01]

C = 0.0000000000000000E+00

std err squared: 0.00000E+00

t-stat: NAN

p-stat: NAN

95% confidence intervals: [0.00000E+00, 0.00000E+00]

G = 9.6094939267681241E+00


t-stat: 6.12557E+01

p-stat: 3.26406E-14

95% confidence intervals: [9.25995E+00, 9.95903E+00]

Coefficient Covariance Matrix

[ 0.61294855 -14.57252165 0. 149.73683951]

[ -14.57252165 498.30241139 0. -5960.28894189]

[ 0. 0. 0. 0.]

[ 149.73683951 -5960.28894189 0. 76524.43521256]


Error Listing

Independent Data Dependent Data Predicted Abs Error Rel Error

0.000E+00 4.450E-02 4.4802945382E-02 3.029454E-04 6.807761E-03

1.790E-02 6.300E-02 6.2767412334E-02 -2.325877E-04 -3.691868E-03

3.480E-02 8.300E-02 8.2554045564E-02 -4.459544E-04 -5.372945E-03

4.890E-02 1.010E-01 1.0116257493E-01 1.625749E-04 1.609653E-03

6.270E-02 1.210E-01 1.2122510182E-01 2.251018E-04 1.860346E-03

7.410E-02 1.395E-01 1.3917880130E-01 -3.211987E-04 -2.302500E-03

8.630E-02 1.590E-01 1.5977579227E-01 7.757923E-04 4.879197E-03

9.600E-02 1.778E-01 1.7717276076E-01 -6.272392E-04 -3.527780E-03

1.067E-01 1.970E-01 1.9741201133E-01 4.120113E-04 2.091428E-03

1.156E-01 2.155E-01 2.1508466822E-01 -4.153318E-04 -1.927294E-03

1.256E-01 2.358E-01 2.3584968324E-01 4.968324E-05 2.107008E-04

1.339E-01 2.540E-01 2.5381443873E-01 -1.855613E-04 -7.305562E-04

1.429E-01 2.730E-01 2.7404239318E-01 1.042393E-03 3.818290E-03

1.503E-01 2.920E-01 2.9125737093E-01 -7.426291E-04 -2.543250E-03


Error Statistics

Absolute Error Relative Error

Minimum: -7.426291E-04 -5.372945E-03

Maximum: 1.042393E-03 6.807761E-03

Mean: -1.349853E-13 8.437023E-05

Std. Error of Mean: 1.394167E-04 9.552160E-04

Median: -6.793901E-05 -2.599277E-04

Variance: 2.526813E-07 1.186169E-05

Standard Deviation: 5.026741E-04 3.444080E-03

Skew: 4.748285E-01 3.138847E-01

Kurtosis: -6.211260E-01 -8.904169E-01


Data Statistics

X Y

Minimum: 0.000000E+00 4.450000E-02

Maximum: 1.503000E-01 2.920000E-01

Mean: 8.540714E-02 1.682929E-01

Std. Error of Mean: 1.269906E-02 2.131391E-02

Median: 9.115000E-02 1.684000E-01

Variance: 2.096461E-03 5.905674E-03

Standard Deviation: 4.578712E-02 7.684838E-02

Skew: -3.284659E-01 -1.894040E-03

Kurtosis: -1.042620E+00 -1.214823E+00


Source Code in C++

// To the best of my knowledge this code is correct.

// If you find any errors or problems please contact

// me directly using [email protected].

//

// James

#include <math.h>

// Fitting target: lowest sum of squared absolute error

// Fitting target value = 3.53753774427e-06

double Miscellaneous_PhysicistPeterCustomEquation_model(double x_in)

{

double temp;

temp = 0.0;

// coefficients

double A = 4.4802945381686374E-02;

double B = 9.1759653506420780E-01;

double C = 0.0000000000000000E+00;

double G = 9.6094939267681241E+00;

temp = A + B*(x_in-C) + 0.5*G*pow(x_in-C, 2.0);

return temp;

}


Source Code in Java




//

// James

import java.lang.Math;



class Miscellaneous_PhysicistPeterCustomEquation

{


{

double temp;

temp = 0.0;

// coefficients

double A = 4.4802945381686374E-02;

double B = 9.1759653506420780E-01;

double C = 0.0000000000000000E+00;

double G = 9.6094939267681241E+00;

temp = A + B*(x_in-C) + 0.5*G*Math.pow(x_in-C, 2.0);

return temp;

}

}


Source Code in JavaScript




//

// James



function Miscellaneous_PhysicistPeterCustomEquation_model(x_in)

{

var temp;

temp = 0.0;

// coefficients

var A = 4.4802945381686374E-02;

var B = 9.1759653506420780E-01;

var C = 0.0000000000000000E+00;

var G = 9.6094939267681241E+00;

temp = A + B*(x_in-C) + 0.5*G*Math.pow(x_in-C, 2.0);

return temp;

}


Source Code in Python

# To the best of my knowledge this code is correct.

# If you find any errors or problems please contact

# me directly using [email protected].

#

# James

import math

# Fitting target: lowest sum of squared absolute error

# Fitting target value = 3.53753774427e-06

def Miscellaneous_PhysicistPeterCustomEquation_model(x_in):

temp = 0.0

# coefficients

A = 4.4802945381686374E-02

B = 9.1759653506420780E-01

C = 0.0000000000000000E+00

G = 9.6094939267681241E+00

temp = A + B*(x_in-C) + 0.5*G*math.pow(x_in-C, 2.0)

return temp


Source Code in C#




//

// James

using System;



class Miscellaneous_PhysicistPeterCustomEquation

{


{

double temp;

temp = 0.0;

// coefficients

double A = 4.4802945381686374E-02;

double B = 9.1759653506420780E-01;

double C = 0.0000000000000000E+00;

double G = 9.6094939267681241E+00;

temp = A + B*(x_in-C) + 0.5*G*Math.Pow(x_in-C, 2.0);

return temp;

}

}


Source Code in SCILAB




//

// James



function y = Miscellaneous_PhysicistPeterCustomEquation_model(x_in)

temp = 0.0;

// coefficients

A = 4.4802945381686374E-02;

B = 9.1759653506420780E-01;

C = 0.0000000000000000E+00;

G = 9.6094939267681241E+00;

temp = A + B*(x_in-C) + 0.5*G*power(x_in-C, 2.0);

y = temp;

endfunction


Source Code in MATLAB

% To the best of my knowledge this code is correct.

% If you find any errors or problems please contact

% me directly using [email protected].

%

% James

% Fitting target: lowest sum of squared absolute error

% Fitting target value = 3.53753774427e-06

function y = Miscellaneous_PhysicistPeterCustomEquation_model(x_in)

temp = 0.0;

% coefficients

A = 4.4802945381686374E-02;

B = 9.1759653506420780E-01;

C = 0.0000000000000000E+00;

G = 9.6094939267681241E+00;

temp = A + B.*(x_in-C) + 0.5.*G.*power(x_in-C, 2.0);

y = temp;


Source Code in VBA

' To the best of my knowledge this code is correct.

' If you find any errors or problems please contact

' me directly using [email protected].

'

' James

' Fitting target: lowest sum of squared absolute error

' Fitting target value = 3.53753774427e-06

Public Function Miscellaneous_PhysicistPeterCustomEquation_model(x_in)

temp = 0.0

' coefficients

Const A = 4.4802945381686374E-02

Const B = 9.1759653506420780E-01

Const C = 0.0000000000000000E+00

Const G = 9.6094939267681241E+00

temp = A + B*(x_in-C) + 0.5*G*Application.WorksheetFunction.power(x_in-C, 2.0)

Miscellaneous_PhysicistPeterCustomEquation_model = temp

End Function


Histogram of shifted time T (seconds)


Histogram of coordinate Y (meters)


Histogram of Absolute Error


Histogram of Relative Error


Histogram of Percent Error


Absolute Error vs. shifted time T (seconds)


Absolute Error vs. coordinate Y (meters)


Relative Error vs. shifted time T (seconds)


Relative Error vs. coordinate Y (meters)


Percent Error vs. shifted time T (seconds)


Percent Error vs. coordinate Y (meters)


coordinate Y (meters) vs. shifted time T (seconds)


shifted time T (seconds) vs. coordinate Y (meters)


coordinate Y (meters) vs. shifted time T (seconds) with model


coordinate Y (meters) vs. shifted time T (seconds) with 95% confidence intervals


phy lab 1

Documents

nan pstat

confidence intervals

abs error rel error

error rmse

model fstatistic pvalue

degrees of freedom regression

model loglikelihood

fit statisticsmost statstics